Heat oil in a soup pot over medium heat. Add onion and saute until it starts to turn translucent, about 2-3 minutes.
Add celery and carrot and saute 2 minutes more.
Add split peas, stock or water, basil and the bay leaf. Bring to boil, cover, reduce flame to low and simmer for 1 to 1 1/2 hours, stirring occasionally.
Season to taste with salt or vegetable salt seasoning the last 5 minutes of cooking.
Salt is not included in nutrition analysis.